To manufacture curved or bent extruded sections or profiles which are generally composed of aluminum and magnesium alloys as required for various purposes in different industrial fields, it is known from EP 0 706 843 B1 to provide an extruder for hollow products with large wall thickness differences that applies force at least at defined distances from the die outlet or counterbeam, using a pressure medium which produces a reaction effect upon the profile or section shaped in the extruder die. The pressing means can be a pressing roller or a sliding surface generating a transverse force or a roller cage. Independently of the pressure applying means which is used to bring about the reaction force, a certain distance must be maintained if the extruded product is to be bent or curved simultaneously with or directly after shaping by the extrusion process in such manner that the workpiece cross sections formed in the extrusion die do not emerge parallel to one another from the die but rather are assume an angle to one another. With this arrangement it is however not possible to produce sections with small bending radii.